Question

A thin half ring of radius $R=20$ cm is uniformly charged with a total charge $q=0.70$nC. The magnitude of electric field strength at the curvature centre of this half ring is

• A. $100V/m$
• B. $20V/m$
• C. $225V/m$
• D. $4V/m$

Answer 1

The correct option is A $100V/m$

Consider a small segment subtending angle $d\theta$
Also, linear charge density $=q/\left(\pi R\right)$
Now, Electric field at center due to small segment is given by,
$E=k\left(\lambda Rd\theta \right)/R^2\times sin\theta$
$=kq/\left(\pi R^2\right)\times sin\theta d\theta$
Therefore, total electric field,
$=kq/\left(\pi R^2\right){\int }_0^{\pi }sin\theta d\theta =2kq/\left(\pi R^2\right)\approx 100V/m$